A tiny, climate-conscious player is creating a giant headache for Big Oil

Exxon Mobil Corp., once a global superpower that could bend governments to its will, is locked in a battle against an upstart investor that wants to shake up the oil giant’s board.

The investor, Engine No. 1, has a stake valued at about $50 million, making it a niche player at the $253 billion company. But it has rallied a critical mass of institutional support to do what decades of environmental and shareholder activism never could: put Exxon Mobil on defense.